I think Tolkien’s perfect proto-McGilchrist form is found in Rivendell and Lorien, the last kingdoms of the elves. The elves, I believe, display the proper relationship between the hemispheres, almost to perfection: the musical and poetic and playful nature of the right hemisphere served by the more mundane functions of the left hemisphere.
The elf could mesmerize by singing with a harp, then put it down to kill an orc with a sword.
It is, I believe, a perfect illustration of the master right hemisphere dispatching his emissarial left hemisphere. After the task is done, the harp is picked back up and the left hemisphere (with its tools of practical skills and control) relaxes at his master’s feet until called upon again.